Given $ m \angle RPS = 2x + 19$, $ m \angle QPR = 6x - 39$, and $ m \angle QPS = 140$, find $m\angle RPS$. $P$ $Q$ $S$ $R$
Explanation: From the diagram, we see that together ${\angle QPR}$ and ${\angle RPS}$ form ${\angle QPS}$ , so $ {m\angle QPR} + {m\angle RPS} = {m\angle QPS}$ Substitute in the expressions that were given for each measure: $ {6x - 39} + {2x + 19} = {140}$ Combine like terms: $ 8x - 20 = 140$ Add $20$ to both sides: $ 8x = 160$ Divide both sides by $8$ to find $x$ $ x = 20$ Substitute $20$ for $x$ in the expression that was given for $m\angle RPS$ $ m\angle RPS = 2({20}) + 19$ Simplify: $ {m\angle RPS = 40 + 19}$ So ${m\angle RPS = 59}$.